I use Wix for my website and decided to go with their built-in eCommerce platform. I have an old, dormant Etsy shop and looked a bit into some others (Red bubble, Shopify) but sticking with Wix was easiest and keeps it all in my own domain. It’s not the most robust service but I just need a platform to get started for now.

It looks like Jake Parker uses Shopify and Will Terry uses Etsy, both of which seem pretty streamlined within their websites. I can’t tell what Lee is using, but it looks kind of like my Wix shop. (I just figured if they all used a certain one that might be a good bet).

I think it doesn’t matter all that much which one you choose so long as the service is reputable and you are not trying to use the platform for exposure, but it sounded from your message like you aren’t trying to sell huge volumes of goods.

I’d check reviews of Woocommerce (I know nothing about them) and if they seem good and it’s the easiest thing to go with then do it! Especially if they integrate well with your site, as @jimsz said!